APPROXIMATE EXPRESSIONS FOR THE REFLECTION COEFFICIENT AT THE OPEN END OF CYLINDRICAL DUCTS TERMINATED BY FLANGES OF FINITE SIZE

摘要

Estimating the magnitude of the pressure reflection coefficient |R| and the end correction l at the open end of ducts is a critical procedure when designing or predicting the acoustic behavior of piping systems, such as exhausts, tailpipes, mufflers and so on. For cylindrical ducts and plane waves, exact intricate solutions exist for two distinct open-end boundary conditions, namely for a thin-walled unflanged pipe and for a pipe terminated by an infinite flange. This work provides simple approximate expressions for |R| and l of cylindrical pipes terminated by circular flanges with finite radii. The expressions are obtained from a polynomial fit performed over the numerical results provided by a Boundary Element model, and is valid for Helmholtz numbers in the range 0 ≤ ka ≤ 3.0, as well as for 0 ≤ a/b ≤ 1, where a and b are the pipe and flange radii, respectively. When compared with both the exact solutions for the unflanged and the infinite-flanged pipe, the approximate formulae provide a maximum error ～ 2% for ka → 3.0.